Hi all, I made another flashcard set. This time for memorizing Quantifiers. Flashcards are what really helped me in undergrad and so I decided to make them to companion my 7sage studies. Thought I'd share to help others who would benefit :) made a folder that I will most likely add more sets to as I go. Much Love and happy studying! https://quizlet.com/user/ehoffmanwallace/folders/lsat-7sage-flashcards
Or is the “tempting but incorrect negation” not saying that the above mentioned is incorrect, but the following statement is??? Lord, ima have a seizure 😂
Wait. Some unicorns poop rainbows is negated to No unicorns poop rainbows and is shown as (U->/PR). Wouldn't it be shown as /U->PR? This doesn't make total sense to me.
"No" would mean you have to negate a concept and make that concept the necessary condition. So "no unicorns poop rainbows" is equivalent to U->/PR.
/U->PR is the same as saying "if one is not a unicorn, then one poops rainbows.," which doesn't follow from the claim because we don't know anything about non-unicorns.
wait so are "some," "most, "many," quantifiers also conditionals? i.e. is "some unicorns dont poop rainbows" a conditional statement? or is it something completely different #help
@rc39 the quantifier words help identify the scope of the conditional. your if/then statement is your conditional, but the quantifier just specifies how often it occurs, or how much of any group is included within the conditional.
the statement "some unicorns don't poop rainbows" is a conditional statement, but the quantifier itself is not a conditional.
@tteokkim surgical explanation and i really appreciate it. you helped clarify some confusion working through this section. We may be looking at a conditional, but the quantifier is NOT conditional--it expresses an intersection. THANK YOU!
So negating isn’t saying no to the argument, it’s just saying “you forgot to look at it this way.” If you’re saying “it’s not the case that some unicorns poop rainbows,” then what you’re saying is there are no unicorns that poop rainbows. If not some, then none. You can’t say “if not some then most” because that’s not negating but adding onto the original claim. You can’t say “if not some then all” because again, that’s saying more than what the claim gives you evidence for.
Instead, negating is just saying “aha you forgot that there are some unicorns that DON’T poop rainbows!” A better view, for me, of negation is not “denying” or “negating” the original claim, but thinking of the possibilities that the claim didn’t originally consider.
No, the negation of most is simply not most. There's a lesson where they go into it, but most implies in a hefty margin that something is greater than 50% and possibly by a larger share than that.
We can picture it on a rough scale of "50% < x <= 100%", where most is greater than half and can technically be all.
Few, on the other hand, implies that it is more than one (or possibly two, it's very vague) and less than one half. This is because few implies a really weird definition of "some but not many", a definition which highlights a more constricted view. With this, we can pinpoint a scale of "1 or 2 < x < many", with a rough indicator on your interpretation of many. However, this indication typically means it is less than half, so you could write the scale as "1 or 2 < x < 50%".
When looking at this, although a mathematical view could imply the negation of most as few, after all, "1 - 'most'" would leave you with a minority, there is a vague margin on what that would actually mean. As well, few is not inclusive to 1/2, meaning defining the negation of many as "few" would confuse an opposite for a negation.
Think back to the really early example of "the room is hot". The opposite of that statement would be "the room is cold", but would that be the negation? There's a range of temperatures that are not hot, like lukewarm, chilly, or freezing that aren't hot, and definitely aren't a strict cold. Because of this, the negation of "the room is hot" is simply "the room is not hot".
Think of the examples of most in a similar manner, where the negation of us saying "most penguins wear tuxedos" could not be "few penguins wear tuxedos". The language simply isn't inclusive to other possibilities, where no penguins wear tuxedos or exactly half of the penguins wear tuxedos. The only reasonable resolution is that it isn't the case that most penguins wear tuxedos.
TDLR: Few isn't inclusive to other possibilities in the range that the negation of most requires, but could be interpreted as an opposite, just not a negation.
since "all A are B" already includes the possibility of "some A are B" (because some could include all), so your answer would not entirely negate it.
additionally, I think that "many A are B" negated is just /(A ‑m→B), or, "it is not the case that many A are B". This way it doesn't necessitate that some A are not B, as the word "few" would.
What is an example of a question type we will encounter where having the negation of an intersection question is going to help us identify the correct answer?
The contrapositive of a conditional statement is created by flipping the order of the statement and negating both parts. It is logically equivalent to the original — meaning if one is true, so is the other.
On the other hand, negation simply means stating that the original statement is not true. It is not logically equivalent — instead, it expresses the opposite.
So, while the contrapositive preserves the truth of the original statement, negation challenges or contradicts it.
I still have a question. Do "all" statements always negate differently than group 1 conditional indicator statements? From my understanding of the material, this is how an all statement negates:
A some arrow /B
And this is how a conditional statement negates:
A and /B
But I think where I'm still confused is whether these are interchangeable since all is a group 1 indicator? I just want to know, if I see a group 1 indicator or an all statement on the LSAT, which translation I should use to get the right answer of if using either is fine.
During the skill builder exercises, the all statements where negated with both the some arrow and the and /, so I am guessing he's trying to say that both are correct. Like when you translate any other relationship with it's contrapositive, when translating the negation relationship you probably need to make a note that it could also mean both.
Yes, but "few" does not have its own expression in lawgic.
For example, think about the sentence "Few children are able to speak spanish."
"Few" implies that there is at least one child, and no more than half of children can speak spanish, or else most children would be able to speak spanish. Thus, this sentence translates into lawgic like this:
#feedback I wish there was a diagram at the end of this lesson with all the conditionals and their negations. It would be helpful to have an overall visual comparison.
The way I think about it is that a contrapositive is a rule that the relationship has to follow vs a negation is a condition/situation that makes the relationship false.
When we look to obtain the contrapositive, we maintain the conditional relationship and just give ourselves another perspective to look at the relationship from vs when we do the negation, we're trying to poke holes in the argument and find a situation that would make the relationship invalid.
I believe this also adds to the conversation, but there was a lesson that I watched on here that explained negation v. opposition that was helpful to understand negating statements
Negation: Contradiction
Opposition: Opposite
Example:
Negation: Rich - Comfortable, Poor, Middle Class (Anything that contradicts being rich, or like you said, "trying to poke holes in the argument and find a situation")
or you can capture the negation without putting all the examples:
A conditional relationship is when one set is completely inside another set, such as a subset inside a superset. The example they always give is "If Jedi, then Force" where Jedi is the subset, and it is completely encapsulated by the superset Force. An intersection is when 2 sets overlap but not completely. Think of a Venn diagram - we are only talking about the middle part where both sets overlap.
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71 comments
Hi all, I made another flashcard set. This time for memorizing Quantifiers. Flashcards are what really helped me in undergrad and so I decided to make them to companion my 7sage studies. Thought I'd share to help others who would benefit :) made a folder that I will most likely add more sets to as I go. Much Love and happy studying! https://quizlet.com/user/ehoffmanwallace/folders/lsat-7sage-flashcards
Why is the negation of Some unicorns poop rainbows not no unicorns poop rainbows
BUT
Some mice are fat can be negated into no mice are fat or all mice are not fat?
I’m very confused on why this has changed. Please please help!
Or is the “tempting but incorrect negation” not saying that the above mentioned is incorrect, but the following statement is??? Lord, ima have a seizure 😂
@Bbqboi the negation of some unicorns poop rainbows is no unicorns poop rainbows
@Bbqboi yes exactly
@GennaBishop bless you 😂
So would the negation of Most Japanese whiskeys are expensive.
JW -m→ E be:
Zero to exactly half of Japanese whiskeys are expensive?
@Jcruzmed Yes
Wait. Some unicorns poop rainbows is negated to No unicorns poop rainbows and is shown as (U->/PR). Wouldn't it be shown as /U->PR? This doesn't make total sense to me.
@AnnieCastillo remember group 4 indicators:
"No" would mean you have to negate a concept and make that concept the necessary condition. So "no unicorns poop rainbows" is equivalent to U->/PR.
/U->PR is the same as saying "if one is not a unicorn, then one poops rainbows.," which doesn't follow from the claim because we don't know anything about non-unicorns.
wait so are "some," "most, "many," quantifiers also conditionals? i.e. is "some unicorns dont poop rainbows" a conditional statement? or is it something completely different #help
@rc39 the quantifier words help identify the scope of the conditional. your if/then statement is your conditional, but the quantifier just specifies how often it occurs, or how much of any group is included within the conditional.
the statement "some unicorns don't poop rainbows" is a conditional statement, but the quantifier itself is not a conditional.
@tteokkim surgical explanation and i really appreciate it. you helped clarify some confusion working through this section. We may be looking at a conditional, but the quantifier is NOT conditional--it expresses an intersection. THANK YOU!
I just want to wish everyone the knowledge and determination to master all of this content and crush the LSAT!!
So negating isn’t saying no to the argument, it’s just saying “you forgot to look at it this way.” If you’re saying “it’s not the case that some unicorns poop rainbows,” then what you’re saying is there are no unicorns that poop rainbows. If not some, then none. You can’t say “if not some then most” because that’s not negating but adding onto the original claim. You can’t say “if not some then all” because again, that’s saying more than what the claim gives you evidence for.
Instead, negating is just saying “aha you forgot that there are some unicorns that DON’T poop rainbows!” A better view, for me, of negation is not “denying” or “negating” the original claim, but thinking of the possibilities that the claim didn’t originally consider.
Very Helpful!
Helpful summary!
Is "few" a negation of "most"?
No, the negation of most is simply not most. There's a lesson where they go into it, but most implies in a hefty margin that something is greater than 50% and possibly by a larger share than that.
We can picture it on a rough scale of "50% < x <= 100%", where most is greater than half and can technically be all.
Few, on the other hand, implies that it is more than one (or possibly two, it's very vague) and less than one half. This is because few implies a really weird definition of "some but not many", a definition which highlights a more constricted view. With this, we can pinpoint a scale of "1 or 2 < x < many", with a rough indicator on your interpretation of many. However, this indication typically means it is less than half, so you could write the scale as "1 or 2 < x < 50%".
When looking at this, although a mathematical view could imply the negation of most as few, after all, "1 - 'most'" would leave you with a minority, there is a vague margin on what that would actually mean. As well, few is not inclusive to 1/2, meaning defining the negation of many as "few" would confuse an opposite for a negation.
Think back to the really early example of "the room is hot". The opposite of that statement would be "the room is cold", but would that be the negation? There's a range of temperatures that are not hot, like lukewarm, chilly, or freezing that aren't hot, and definitely aren't a strict cold. Because of this, the negation of "the room is hot" is simply "the room is not hot".
Think of the examples of most in a similar manner, where the negation of us saying "most penguins wear tuxedos" could not be "few penguins wear tuxedos". The language simply isn't inclusive to other possibilities, where no penguins wear tuxedos or exactly half of the penguins wear tuxedos. The only reasonable resolution is that it isn't the case that most penguins wear tuxedos.
TDLR: Few isn't inclusive to other possibilities in the range that the negation of most requires, but could be interpreted as an opposite, just not a negation.
Fellow gamecock on here. Comment was at the top of my screen. Just wanted to pay respect to the username!
Spurs up! Go cocks!!
can it be true to say that 'some' includes 'many' and 'all' and when negating they will all revert back to the same negation of 'none'?
no thats wrong
Some A are B- negation: no A are B
All A are B - negation: some A are B
Many A are B- negation: few A are B
^ I think thats accurate
wouldnt it be
All A are B – negation: some A are /B
since "all A are B" already includes the possibility of "some A are B" (because some could include all), so your answer would not entirely negate it.
additionally, I think that "many A are B" negated is just /(A ‑m→B), or, "it is not the case that many A are B". This way it doesn't necessitate that some A are not B, as the word "few" would.
Any feedback is appreciated :)
What is an example of a question type we will encounter where having the negation of an intersection question is going to help us identify the correct answer?
^^^ in what cases should we negate on the test?
What's the difference between a negation and a contrapositive?
The contrapositive of a conditional statement is created by flipping the order of the statement and negating both parts. It is logically equivalent to the original — meaning if one is true, so is the other.
On the other hand, negation simply means stating that the original statement is not true. It is not logically equivalent — instead, it expresses the opposite.
So, while the contrapositive preserves the truth of the original statement, negation challenges or contradicts it.
Sometimes I feel like I learn more from the comment section.
I still have a question. Do "all" statements always negate differently than group 1 conditional indicator statements? From my understanding of the material, this is how an all statement negates:
A some arrow /B
And this is how a conditional statement negates:
A and /B
But I think where I'm still confused is whether these are interchangeable since all is a group 1 indicator? I just want to know, if I see a group 1 indicator or an all statement on the LSAT, which translation I should use to get the right answer of if using either is fine.
During the skill builder exercises, the all statements where negated with both the some arrow and the and /, so I am guessing he's trying to say that both are correct. Like when you translate any other relationship with it's contrapositive, when translating the negation relationship you probably need to make a note that it could also mean both.
#feedback Can you translate the negation of the word "rarely" (not rarely) to "frequently"?
#help isn't 'few' another intersection relationship?
Yes, but "few" does not have its own expression in lawgic.
For example, think about the sentence "Few children are able to speak spanish."
"Few" implies that there is at least one child, and no more than half of children can speak spanish, or else most children would be able to speak spanish. Thus, this sentence translates into lawgic like this:
C ←s→ SS (some children speak spanish)
C ‑m→ /SS (most children can not speak spanish)
#feedback I wish there was a diagram at the end of this lesson with all the conditionals and their negations. It would be helpful to have an overall visual comparison.
confused why the some negative isn't the same as in previous lesson:
Original: P ←s→ C
Negated: /(P ←s→ C)
Negated: P → /C
Am I missing something? how the excerpt above become incorrect negation for unicorns and poop example?
This :U ←s→ /PR
Is Not the same as: /(UPR
What is the difference between a conditional statement that is negated vs its contrapositive? I'm having a hard time grasping the two concepts.
#feedback #help
The way I think about it is that a contrapositive is a rule that the relationship has to follow vs a negation is a condition/situation that makes the relationship false.
When we look to obtain the contrapositive, we maintain the conditional relationship and just give ourselves another perspective to look at the relationship from vs when we do the negation, we're trying to poke holes in the argument and find a situation that would make the relationship invalid.
Negated: NOT logically identical
Poor vs Not poor
No pilots are blind vs some pilots are blind
This vs Not this
Contrapositive: Logically identical statements
When a dog is happy, it wags its tail vs. When a dog doesn't wag its tail, it is not happy
We use negated statements to form contrapositives.
I like to thing of negated as making it not true, whereas contrapositive is more like reversing it.
If you like math, you can kinda compare it to how opposites and inverse are two very different concepts.
The opposite of 4 is -4. The inverse of 4 is 1/4.
The opposite of A->B is whatever makes A->B NOT true.
The contrapositive of A->B is /B->/A. It doesn't affect the truth of the previous statement at all, they both coexist.
i hate math lol but thank you anyways for trying to help!
thank you this just helped me a lot!
I love the sentiment of poking holes in the argument. I understand this completely now!
I believe this also adds to the conversation, but there was a lesson that I watched on here that explained negation v. opposition that was helpful to understand negating statements
Negation: Contradiction
Opposition: Opposite
Example:
Negation: Rich - Comfortable, Poor, Middle Class (Anything that contradicts being rich, or like you said, "trying to poke holes in the argument and find a situation")
or you can capture the negation without putting all the examples:
Rich - not rich
Opposition: Hot- Cold (Just the opposite)
Really like this approach as well! Mine is a lot less sophisticated, but based on our lessons so far I differentiate the two by:
Negating: It is not the case that [statement] --> falsifying
Contrapositive: It can also be said that [statement] --> still true
is this the correct negation of the most stamens provided as an example?
EX: Most Japanese whiskeys are expensive
original: Most J are E
negated: anywhere from 0 to half of J are E
English: anywhere from 0 to half of japeNeese whiskeys are expensive
Yes, that's right.
#help
for the part that says "Negated: No unicorns poop rainbows. U → /PR" why isnt it /U->PR?
That would mean not being a unicorn is sufficient for pooping rainbows which is not the negation of the original.
Can someone give another explanation for the difference between conditionals and intersections? The one provided here still confuses me. Thanks!
A conditional relationship is when one set is completely inside another set, such as a subset inside a superset. The example they always give is "If Jedi, then Force" where Jedi is the subset, and it is completely encapsulated by the superset Force. An intersection is when 2 sets overlap but not completely. Think of a Venn diagram - we are only talking about the middle part where both sets overlap.
The simplest way I see it without any terminology or anything confusing is like this :
Conditional = a contract, like you gotta do this or else (if you are a unicorn, then you poop rainbows)
Intersection = something that just happens to be the case (some unicorns poop rainbows)
Conditional means a law or a mandate, whereas an intersection is more of a characteristic. Another example below:
Conditional: If it is 100 degrees, then one wears a linen shirt
Intersection: Some people wear linen shirts when it is 100 degrees
Any reason why the last example is not negated?
It's not the case that most Japanese whiskeys are expensive.
= 50% or less of Japanese whiskeys are expensive
(i think)
Would it be correct for the negation of U --> PR to be /U --> PR? #help
The correct negation for "Some unicorns poop rainbows. U ←s→ PR"
as shown above, is U→/PR.
No unicorns poop rainbows, or if you are a unicorn you don't poop rainbows.
Doesn't that translate into "If you are not a unicorn, then you defecate rainbows" ?